Graphical User Interface for Modifying Structables and their Mosaic Plots

Transcription

1 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 1 Graphical User Interface for Modifying Structables and their Mosaic Plots Richard M. Heiberger and Temple University Erich Neuwirth University of Vienna A structable object is a representation in R of a k-dimensional contingency table. The structable object has two attributes: split vertical that carries information on assignment of the factors to row or columns, and dnames that carries information on sequencing of the factors. The printed display of a structable as a flat table in two dimensions shows the row and column assignment but is unable to illustrate the joint sequencing of the horizontal and vertical splits. The default plot of a structable is as a mosaic plot with recursive splits of the factors in the specified sequence and according to the orientation given in split vertical. Each split is along the vertical or horizontal direction associated with the column or row assignment of its factor.

2 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 2 Germangrade Gender Mathgrade female male Figure 1: In the left panel we show a three-factor contingency table displayed as a structable. In the right panel we show a mosaic plot of the same data. The mosaic uses the default configuration, conditioning first on the outer rows showing Gender, then on the columns showing Germangrade nested within Gender, and finally on the inner rows showing Mathgrade nested within Germangrade nested within Gender.

3 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 3 1 Example StudentData and Pivot Table by RExcel The StudentData (Neuwirth, 2011) contains measurements on 1126 Austrian undergraduates collected over a ten year period. We will look at three of the factors here. Gender: Student s Gender: m for man and w for woman. Mathgrade: Discrete values (1, 2, 3, 4) with 1 as the best grade. Germangrade: Discrete values (1, 2, 3, 4) with 1 as the best grade. We can construct a contingency table for these factors as a pivot table in Excel and then export it directly to a structable in R (Figure 2), or we can construct the structable directly in R(Figure 3). Either way we have the same structable, called GGM here.

4 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 4 Figure 2: Pivot table in Excel that was constructed from the original data (one observation per student) and then exported to R using the RExcel Put Pivottable context menu item.

5 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 5 > GGM <- structable(~ Gender + Germangrade + Mathgrade, StudentData) > GGM Germangrade Gender Mathgrade female male > Figure 3: Construction of structable in R with the structable function on the dataframe containing the original data (one observation per student).

6 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 6 > mosaicpermdialog(ggm) [1] "mosaic(ggm)" > a. R command line b. Rcmdr menu from Rcmdr window c. Rcmdr menu from Excel (all platforms) (all platforms) (Windows only) Figure 4: Three equivalent ways to start the mosaic dialog shown in Figure 5.

7 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 7 Figure 5: Initial dialog box and mosaic display. The labeled rows of buttons in the dialog box show the sequence of splits illustrated in the mosaic plot. The columns of labels in the dialog box show the assignment of factors to the rows and columns of the structable and mosaic plot. The arrow buttons indicate the specification of split sequence and row/column assignment that are possible from the current display.

8 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 8 The printed representation of a structable displays only the separate derived sequencing of the horizontal and vertical factors. As a consequence, multiple structables and their associated mosaic plots can yield the same printed flat table. We have developed a graphical user interface, and corresponding R functions, that simplify the specification of the alternate sequencing of splits hence associated mosaic plots consistent with a printed flat table. The user interface also permits rearrangement of the flat table, either by reassigning factors to rows or columns or by changing the order of the factors within the same row or column assignment. The primary R function is an aperm (array permutation) method designed for structables.

9 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 9 Figure 6: For this and the remaining figures in the paper, we clicked the Colorize last variable checkbox. The coloring matches the last split, Mathgrade here. We click the German Down arrow to get Figure 7.

10 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 10 Figure 7: Gender is still the first split. In this figure Mathgrade is the second split. The coloring matches the last split, Germangrade here. We click the Gender Down arrow to get Figure 8.

11 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 11 Figure 8: The structable for this figure (Figure 8) is identical to the structable for Figures 6 and 7. The structable is displayed in Figure 11. In all three of these figures, the areas of the rectangles corresponding to each count in the structable are proportional to the count. The interpretation as conditional probabilities of this plot (distribution of Gender by MathGrade conditional on GermanGrade) doesn t make much sense, where the similar interpretation of the other two plots as distributions of the two grades conditional on Gender does make sense.

12 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth Figure 9: All three mosaic plots that correspond to the same flat display of their structable. The conditioning of the splits differs. The relative position of each cell of the three-way table is the same.

13 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 13 Figure 10: In this figure, we moved Gender from a row factor to a column factor. Now the flat structable has a different appearance.

14 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 14 Figure 11: The dialog box can return either the structable object or the function call that generates the structable object.

15 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 15 Salk Vaccine (Chin et al, 1961), also in(agresti, 1990) and in(heiberger and Holland, 2004), discuss174poliocasesclassifiedbyageofsubject,whetherornotthesubjectreceived the Salk polio vaccine, and whether the subject was ultimately paralyzed by polio. We wish to learn if symptom status (paralysis or not) is independent of vaccination status after controlling for age.

16 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth no vac no vac no vac no vac no vac no vac no.par par Figure 12: Mantel Haenszel Cochran test for the Salk polio example. It is easy to see from the mosaic plot that the upper right box in each age group is taller than the upper left box in its own age group. That is, the proportion of cases without paralysis in the vaccinated treatment is higher for all age groups.

17 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 17 References Erich Neuwirth(2008), Student data collected in classes, , Distributed on CRAN as part of the RthroughExcelWorkbooksInstaller package (Heiberger and Neuwirth, 2011). Richard M. Heiberger and Erich Neuwirth (2009). R Through Excel: Introductory and Advanced Statistics, Data Analysis, and Graphics with a Spreadsheet Interface and Spreadsheet Tools, Springer, Use R series, ISBN: Richard M. Heiberger (rmh@temple.edu) and Erich Neuwirth (erich.neuwirth@univie.ac.at) (2011). RthroughExcelWorkbooksInstaller: Excel Workbooks supporting Statistics courses using R through Excel. R package version Erich Neuwirth (erich.neuwirth@univie.ac.at) (2011). RExcelInstaller: Integration of R and Excel, (use R in Excel, read/write XLS files). R package version

18 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 18 David Meyer, Achim Zeileis, and Kurt Hornik (2011). vcd: Visualizing Categorical Data. R package version David Meyer, Achim Zeileis, and Kurt Hornik (2006). The Strucplot Framework: Visualizing Multi-Way Contingency Tables with vcd. Journal of Statistical Software, 17(3), Chin, T. W., Hall, E., Gravelle, C., and Speers, J. (1961). The influence of Salk vaccination on the epidemic pattern and spread of the virus in the community, American Journal of Hygiene, 73: Agresti, A. (1990). Categorical Data Analysis. Wiley. Heiberger, R. M. and Holland, B. (2004). Statistical Analysis and Data Display: An Intermediate Course with Examples in S-Plus, R, and SAS. Springer.

19 Graphical User Interface for Modifying Structables and their Mosaic Plots UseR 2011 Heiberger and Neuwirth 19 Table Classes R has 3 classes for tables: table, ftable, and structable. In table, all factors have a joint order and there is no horizontal-vertical orientation. In ftable, factors are divided into two sets, horizontal and vertical, and only ordered within these sets; there is no joint order. In structable, factors are ordered (as in table) and also assigned to either horizonal or vertical (as in ftable). The separate ordering of the horizontal and vertical factors is derived from the joint ordering. structable inherits from ftable, and not table. Since printing a structable and printing an ftable produces typographically equivalent results, this seems to make sense. But the print method hides the joint order. The joint order is important for mosaic plots. table and structable have mosaic plots as their default plot method. ftable does not have a plot method of its own. Plotting an ftable will produce a not very useful scatterplot. In the object hierarchy of R, structable inherits from ftable, and not from table. With respect to the default plotting method, this is a somewhat unfortunate class hierarchy.